Let us pause here to emphasize that there is no tension between this result and the fact that massless planar five-point Feynman integrals with more complicated singularities are certainly known. For example, the two-loop master integrals relevant to five-point functions in massless QCD have a 30-letter symbol alphabet [1]} that indicates the presence of branch point singularities at \(s_{i,i+1} + s_{i+1,i+2} = 0\)  (and other more complicated functions of the Mandelstam variables). This is not a contradiction because our claim, as mentioned above, only applies to the so-called first-type Landau singularities, which can always be expressed in momentum twistor space without reference to a choice of infinity twistor \(\mathcal {I}\) . The fact that the locus \(s_{i,i+1} + s_{i+1,i+2} = 0\)  cannot be expressed without introducing \(\mathcal {I}\)  is a giveaway that these more complicated letters indicate the presence of second-type singularities.
